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Functional linear regression with derivatives

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  • André Mas
  • Besnik Pumo

Abstract

We introduce a new model of linear regression for random functional inputs taking into account the first-order derivative of the data. We propose an estimation method that comes down to solving a special linear inverse problem. Our procedure tackles the problem through a double and synchronised penalisation. An asymptotic expansion of the mean square prevision error is given. The model and the method are applied to a benchmark dataset of spectrometric curves and compared with other functional models.

Suggested Citation

  • André Mas & Besnik Pumo, 2009. "Functional linear regression with derivatives," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(1), pages 19-40.
    • Handle: RePEc:taf:gnstxx:v:21:y:2009:i:1:p:19-40
    DOI: 10.1080/10485250802401046
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    References listed on IDEAS

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    1. Brown P.J. & Fearn T & Vannucci M, 2001. "Bayesian Wavelet Regression on Curves With Application to a Spectroscopic Calibration Problem," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 398-408, June.
    2. Amato, U. & Antoniadis, A. & De Feis, I., 2006. "Dimension reduction in functional regression with applications," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2422-2446, May.
    3. He, Guozhong & Müller, Hans-Georg & Wang, Jane-Ling, 2003. "Functional canonical analysis for square integrable stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 54-77, April.
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    Cited by:

    1. Hao, Siteng & Lin, Shu-Chin & Wang, Jane-Ling & Zhong, Qixian, 2024. "Dynamic modeling for multivariate functional and longitudinal data," Journal of Econometrics, Elsevier, vol. 239(2).
    2. Chiou, Jeng-Min & Yang, Ya-Fang & Chen, Yu-Ting, 2016. "Multivariate functional linear regression and prediction," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 301-312.
    3. Laurent Delsol, 2013. "No effect tests in regression on functional variable and some applications to spectrometric studies," Computational Statistics, Springer, vol. 28(4), pages 1775-1811, August.
    4. Zhenjie Liang & Futian Weng & Yuanting Ma & Yan Xu & Miao Zhu & Cai Yang, 2022. "Measurement and Analysis of High Frequency Assert Volatility Based on Functional Data Analysis," Mathematics, MDPI, vol. 10(7), pages 1-11, April.
    5. Han Shang, 2014. "A survey of functional principal component analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 121-142, April.
    6. Hans-Georg Müller & Wenjing Yang, 2010. "Dynamic relations for sparsely sampled Gaussian processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 1-29, May.
    7. Ahmedou, Aziza & Marion, Jean-Marie & Pumo, Besnik, 2016. "Generalized linear model with functional predictors and their derivatives," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 313-324.
    8. Shang, Han Lin, 2017. "Functional time series forecasting with dynamic updating: An application to intraday particulate matter concentration," Econometrics and Statistics, Elsevier, vol. 1(C), pages 184-200.

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